How do you write an equation for a graph

Question

A graph that is in my homework that I'm having truble with.

Answer 1

OK, with the added information, we can find "a" and finish the solution.  So far, we have

 

y = a(x - 4)² + 40

 

Since (0,0) is on the curve,

 

0 = a(0 - 4)² + 40

0 = 16a + 40

a = -40/16 = - 5/2

 

y = (-5/2)(x - 4)² + 40

 

Let us test this at (8,0)

 

y = (-5/2)(8 - 4)² + 40 = 0  [good]

 

Note the parabola must be concave downward, as Michael explained.

Answer 2

The equation of a parabola is in the form:

 

y = a(x - h)² + k, where (h, k) represents the coordinates of the vertex of the parabola. The value of a will determine whether the parabola is concave up or down. If a > 0, then the parabola will be concave up, or shaped like the letter U. If a < 0, then the parabola will be concave down, or shaped like a frown. 

 

In your problem, the vertex (h, k) is (4, 40).